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1、MeasurementTechniques,Vol.53,No.8,2010ANEWMETHODOFDETERMININGTHEAMPLITUDEANDPHASEOFANALTERNATINGSIGNALP.B.PetrovicandM.P.StevanovicUDC621.3.018Anewmethodofdeterminingtheunknownamplitudesandphasesofanalternatinganalogsignalwithalimitedspectrumisconsidered.Themainparametersofthesigna
2、larereconstructedfromsamplesbasedonanalyticalexpressions.Computermodelingconfirmstheaccuracyoftheproposedalgorithm.Themethodshouldfindapplicationwhenreconstructingasignal,calculatingthespectrum,andtheaccuratemeasurementoftherootmeansquarevalue(ofthepowerandenergy)ofanalternatingsig
3、nal.Keywords:signalreconstruction,VanderMondematrix,Fouriercoefficients,analyticalsolution,simulation.Thereconstructionofsignalsbasedonmeasurementsisthecentralprobleminmanyapplications,connectedwithsignalprocessing.However,thedataavailableareofteninsufficienttoensurehighresolutiono
4、fthereconstruction[1].Manyattemptshavebeenmadetofindanoptimalmethodofdigitizationandforre-establishingafrequency-limitedsignal,whichcanberepresentedintheformofaFourierseries(trigonometricpolynomials).Newmethodsofreconstructingperiodicsignalsbyanonuniformselectionofreadoutshavebeend
5、escribedin[2–5].In[6],astandardmatrixinversionisusedasthemethodofreconstruction,butthisrequiresaconsiderablevolumeofnumericalcalculations.Itwasstatedin[7]that,bythecorrectchoiceofthetimeparameters,whichenablesintegrationtobecarriedout,analternatingsignalcanberepresentedbyaregularma
6、trixformofthesystemofequations.Thisenablesthereconstructionprocesstobecarriedoutmuchmoreeffectively.Ifthereadoutsaretakenwithouterrors,thealgorithmproposedinthepresentpapercanbeusedwithoutanymod-ificationtore-establishaperiodicsignalwithalimitedspectrum.However,inpractice,thereadou
7、tsareobtainedwithacertainerror,i.e.,thesignalisrepresentedbytheaveragevalueintheneighborhoodsofthepointatwhichthesamplingiscarriedout[5].Insuchasituationtheproposedalgorithmhastobemodified,inordertoobtainthebestestimateofthesignalbasedonpreviouslyestablishedcriteria,aswasdonein[5,6
8、,8–11].Inthispaper,wepropo
